Dissipation will depend on the temperature of the thermal bath, and although during inflation everything takes place in the slow-roll, slowly changing regime, what matters is the comparison between the dissipation coefficient \(\Upsilon \)  and Hubble friction \(H\) , given by the ratio \(Q=\Upsilon /3H\) . Typically this ratio is an increasing function of time, and depending on parameters inflation may enter in what is called the strong dissipative regime (SDR), i.e., \(Q \gg 1\)  with dissipation fully dominating the dynamics at the background and perturbative level. Thermal fluctuations must be taken into account [1]}, and when the dissipative coefficient is an increasing function of the temperature \(T\)  this leads to the amplification of the scalar curvature perturbation, and eventually to a blue-tilted spectrum. While we may want to avoid as much as possible this effect on CMB scales, later on before the end of inflation this effect may enhance the spectrum enough to source the tensor at second order and allow the formation of PBHs. The latter has been studied (to our knowledge for the first time) in Ref. [2]} for a dissipative coefficient \(\Upsilon \propto T^3\)  and an inflationary quartic chaotic model. Sufficient enhancement of the primordial spectrum only takes place during the last 10-15 e-folds of inflation, which translates at re-entry in relatively light, evaporating PBHs with masses \(M_{PBH} \lesssim 10^3\)  g. The effect on the tensor spectrum has been studied in Ref. [3]} for a warm quintessential model with a linear and cubic dissipative coefficient. They focused on the enhancement during the kinetion period following warm quintessential inflation. The GW spectrum today would have a large enough amplitude to be detected, but peaked at too large frequencies, by far outside the range of present and future GW detectors. However this conclusion may depend on the functional \(T\)  dependence of the dissipative coefficient, i.e., the pattern of inflaton interactions, and to some extend on the inflationary model. Here we want to extend their analyses and explore other possibilities.
